Elements of geometry, containing books i. to vi.and portions of books xi. and xii. of Euclid, with exercises and notes, by J.H. SmithRivingtons, 1876 - 349 sider |
Inni boken
Resultat 1-5 av 83
Side 13
... ABC , DEF , let AB = DE , and AC = DF , and △ BAC = △ EDF . Then must BC = EF and △ ABC = △ DEF , and the other Ls , to which the equal sides are opposite , must be equal , that is , △ ABC = L DEF and ACB = △ DFE . For , if △ ABC ...
... ABC , DEF , let AB = DE , and AC = DF , and △ BAC = △ EDF . Then must BC = EF and △ ABC = △ DEF , and the other Ls , to which the equal sides are opposite , must be equal , that is , △ ABC = L DEF and ACB = △ DFE . For , if △ ABC ...
Side 16
... ABC , let AC = AB . ( Fig . 1. ) Then must 4 ABC = L ACB . Imagine the △ ABC to be taken up , turned round , and set down again in a reversed position as in Fig . 2 , and designate the angular points A ' , B ' , C. Then in as ABC , A'C ...
... ABC , let AC = AB . ( Fig . 1. ) Then must 4 ABC = L ACB . Imagine the △ ABC to be taken up , turned round , and set down again in a reversed position as in Fig . 2 , and designate the angular points A ' , B ' , C. Then in as ABC , A'C ...
Side 17
... ABC , DEF , let ABC = DEF , and 2 ACB = △ DFE , and BC = EF . Then must AB = DE , and AC = DF , and △ BAC = △ EDF . For if A DEF be applied to AABC , so that E coincides with B , and EF falls on BC ; then . EF = BC , .. F will ...
... ABC , DEF , let ABC = DEF , and 2 ACB = △ DFE , and BC = EF . Then must AB = DE , and AC = DF , and △ BAC = △ EDF . For if A DEF be applied to AABC , so that E coincides with B , and EF falls on BC ; then . EF = BC , .. F will ...
Side 25
... Let AB make with CD upon one side of it the 48 ABC , ABD . Then must these be either two rt . Ls , or together equal to two rt . 4 s . First , if ABC = △ ABD as in Fig . 1 , each of them is a rt . 4 . Secondly , if ABC be not = △ ABD ...
... Let AB make with CD upon one side of it the 48 ABC , ABD . Then must these be either two rt . Ls , or together equal to two rt . 4 s . First , if ABC = △ ABD as in Fig . 1 , each of them is a rt . 4 . Secondly , if ABC be not = △ ABD ...
Side 26
... let the st . lines BC , BD , on opposite sides of AB , make ≤ s ABC , ABD together = two rt . angles . Then BD must be in the same st . line with BC . For if not , let BE be in the same st . line with BC . Then And 2 s ABC , ABE ...
... let the st . lines BC , BD , on opposite sides of AB , make ≤ s ABC , ABD together = two rt . angles . Then BD must be in the same st . line with BC . For if not , let BE be in the same st . line with BC . Then And 2 s ABC , ABE ...
Andre utgaver - Vis alle
Elements of geometry, containing books i. to vi.and portions of books xi ... Euclides,James Hamblin Smith Uten tilgangsbegrensning - 1872 |
Elements of Geometry, Containing Books I. to Vi.And Portions of Books Xi ... James Hamblin Smith,Euclides Ingen forhåndsvisning tilgjengelig - 2022 |
Elements of Geometry, Containing Books I. to VI.and Portions of Books XI ... James Hamblin Smith,Euclides Ingen forhåndsvisning tilgjengelig - 2018 |
Vanlige uttrykk og setninger
AB=DE ABCD AC=DF angles equal angular points base BC BC=EF bisecting the angle centre chord circumference coincide describe diagonals diameter divided equal angles equiangular equilateral triangle equimultiples Eucl Euclid exterior angle given angle given circle given line given point given st given straight line greater than nD hypotenuse inscribed intersect isosceles triangle less Let ABC Let the st lines be drawn magnitudes middle points multiple opposite angles opposite sides parallelogram pentagon perpendicular polygon produced Prop prove Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radius ratio rectangle contained reflex angle rhombus right angles segment shew shewn straight line joining sum of sqq Take any pt tangent THEOREM together=two rt trapezium triangle ABC triangles are equal vertex vertical angle
Populære avsnitt
Side 51 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 38 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Side 178 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Side 46 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon...
Side 50 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.
Side 104 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC.
Side 187 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Side 89 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle, Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one of the sides containing it, let fall the perpendicular AD from the opposite angle.
Side 5 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Side 5 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.